Young Researchers Workshop: Stochastic and deterministic methods in kinetic theory

Stability of dirac masses for simple alignment processes on the sphere

Amic Frouvelle

Paris Dauphine University
[SLIDES]

We study the long-time behaviour of simple kinetic alignment processes on the sphere. Due to the lack of conservation of the center of mass (which is not even well-defined), we do not know in advance where the probability density function is going to concentrate. However, we are able to show that it will actually converge to a dirac mass, and to provide the rate of convergence.